Two delegates of Germany’s far-right party are being investigated by Germany’s state prosecutor over possible incitement to hatred, after one of them accused Cologne police who had tweeted a new year message in Arabic of appeasing “barbaric, gang-raping Muslim hordes of men”.

Beatrix von Storch, the deputy leader of Alternative for Germany (AfD), was also temporarily suspended from Twitter and Facebook as a new law forcing social media companies to remove hate speech came into force in Germany on 1 January.

The authorities are considering whether Von Storch and Weidel should be charged with incitement to hatred..

Von Storch’s Twitter account was suspended for 12 hours over her post. Under the new law known as NetzDG, social media firms face fines of up to €50m (£44m) if they do not remove “obviously illegal” hate speech and other postings within 24 hours of receiving a notification.

Critics of the law, which was conceived by the Social Democrat-run justice ministry, say it will place censorship decisions that require legal training at the whim of technology companies.

Questions have been raised about whether sites such as Twitter will hire enough trained moderators to cope with the expected influx of deletion requests.

Digital rights activists, technology companies and political groups including the pro-business Free Democratic party, the Left party and the far-right AfD have been vocal critics of the new law.

Returning to Twitter after her ban, Von Storch – who posed with the former Ukip leader Nigel Farage when he endorsed AfD’s election campaign in September – posted in German: “Facebook has now also censored me. This is the end of the constitutional state.”

Cologne’s state prosecutor said it had received “several hundred” criminal complaints against Von Storch. If she is charged and found guilty of incitement to hatred, she could face a fine or a prison sentence of up to three years.

A spokesman for Cologne police told Der Spiegel that its investigation into the inflammatory tweets was normal procedure. “If there’s a suspicion that we are dealing with a crime, it is our legal responsibility to act,” he said.

Von Storch previously provoked outrage for her social media activity when she answered “yes” in January 2016 to a question on Facebook asking whether firearms should be used against women and children trying to cross the German border. Von Storch, whose grandfather served as finance minister under Hitler, later claimed her computer mouse had slipped.